Answer
Yes, see explanations.
Work Step by Step
Yes, we can find one or more examples of graphs of $ƒ(x)$ and $g(x)$ that are not straight lines but the graph of $f(g(x))$ is a straight line.
For example, let $f(x)=x^2$ and $g(x)=\sqrt x$; the graphs of these functions are not straight lines. However, their composite $f(g(x))=f(\sqrt x)=(\sqrt x)^2=x$ is a straight line.
More generally, let $f(x)$ be a non-linear one-to-one function; we can find its inverse as $g(x)=f^{-1}(x)$. As the inverse function is a reflection of the original with respect to the line of $y=x$, function $g(x)$ will also be non-linear. By using the properties of inverse functions, we have $f(g(x))=f(f^{-1}(x))=x$, which represents a line.
